Homework

Problem 1 · medium

For x^2/36 + y^2/16 = 1, find: a, b, c, vertices, co-vertices, and foci.

Problem 2 · medium

Write the standard form of an ellipse with center (0,0), vertices (0,±7), and co-vertices (±3,0).

Problem 3 · medium

For (x-1)^2/25 + (y+2)^2/9 = 1, find the center, vertices, and foci.

Problem 4 · medium

Write the equation of the ellipse with foci (±2,0) and vertices (±5,0).

Problem 5 · medium

For x^2/4 - y^2/9 = 1, find: a, b, c, vertices, foci, and asymptotes.

Problem 6 · medium

For y^2/16 - x^2/9 = 1, find the vertices and asymptotes.

Problem 7 · medium

Write the equation of a hyperbola with center (0,0), vertices (±3,0), and foci (±5,0).

Problem 8 · easy

Identify the conic: x^2 + y^2 - 4x + 2y = 0.

Problem 9 · easy

Identify the conic: x^2 - y^2 = 4.

Problem 10 · easy

Identify the conic: 3x^2 + 5y^2 = 15.

Problem 11 · easy

Identify the conic: y = 2x^2 - 3.

Problem 12 · challenge

Convert to standard form and identify: x^2 + 4y^2 - 2x - 16y + 13 = 0.

Problem 13 · challenge

For the hyperbola (x+1)^2/9 - (y-2)^2/16 = 1, state center, vertices, and asymptotes.

Problem 14 · easy

What is the value of c for the ellipse x^2/100 + y^2/36 = 1?

Problem 15 · medium

A planet orbits in an ellipse with the sun at one focus. If a=10 AU and c=6 AU, find b.

Problem 16 · easy

Find the length of the major axis for x^2/49 + y^2/25 = 1.

Problem 17 · medium

Find the foci of y^2/25 - x^2/11 = 1.

Problem 18 · medium

Write the equation of a hyperbola with center (0,0), foci (0,±5), and vertices (0,±3).

Problem 19 · challenge

For what values of k does x^2/k + y^2/4 = 1 represent an ellipse with horizontal major axis?

Problem 20 · medium

An elliptical room is 40 feet long (major axis) and 20 feet wide (minor axis). Where are the foci?

Problem 21 · medium

State the domain and range of the ellipse x^2/16 + y^2/9 = 1.

Problem 22 · easy

For the hyperbola x^2 - y^2 = 1, what are the asymptotes?

Problem 23 · challenge

Complete the square and identify: 9x^2 - 4y^2 - 18x + 16y - 43 = 0.

Problem 24 · challenge

Find b if an ellipse has a=6 (vertical) and passes through (2, 3*sqrt(3)).

Problem 25 · medium

A hyperbola has the equation x^2/25 - y^2/25 = 1. What angle do the asymptotes make with the x-axis?